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Q.

Determine the students' median weight from the following data.

Weight (in Kg)<45<50<55<60<65<70<75
No. of Students251319252830

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a

61.55

b

56.67

c

40.86

d

none

answer is B.

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Detailed Solution

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To calculate the median from the following interval data, we must first compute the cumulative frequencies.

Because the class widths are unequal in this case, we don't need to adjust the interval frequencies.

Weightcf
40- 452
45-505
50-5513
55-6019
60-6525
65-7028
70-7530

We have on the x-axis = the weight of students and on the y-axis= number of students.

N=30 then 302=15

The cumulative frequency just greater than n2 is 19 and the corresponding class is 55–60.

Thus, 55–60 is the median class such that

n2=15,l=55,f=6,cf=13 , and h=5

Substituting these values in the formula

Median, M=l+n2-cff×h

M=55+(15136)×5

M=55+26×5=55+1.67=56.67

 Median =56.67

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